To illustrate the ability to model the tails, we compared the estimated empirical quantile functions. We did so for both marginal distributions (Figure REF ) but also for the distribution of \(\Vert {\mathbf {x}}\Vert _2\)  (Figure REF  in the Appendix).
In line with the findings by [1]}, we notice that the vanilla NF is not capable of modeling the quantiles of the target distribution. More precisely, we observe that the corresponding quantile function is steeper around its center and has shorter tails. This means that the distribution learned by the NF does not account for the heavy tails by directly modeling
them, but instead covers samples from the tails of the data distribution by being more widespread.
In contrast, the base distributions that took the tailedness of \({\mathbf {x}}\)  into account, could achieve a much better fit to the quantiles, see Figure REF  in the Appendix for further results.
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